Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on the fractal dimension

A peer-reviewed open-access journal

PhytoKeys | 13: 79-95 (2018)

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Similarity analysis between species of the genus
Quercus L. (Fagaceae) in southern Italy based on the
fractal dimension

Carmelo Maria Musarella'*, Ana Cano-Ortiz', José Carlos Pifiar Fuentes',
Juan Navas-Urefia?, Carlos José Pinto Gomes*, Ricardo Quinto-Canas**,
Eusebio Cano', Giovanni Spampinato?

I Dpt. of Animal and Plant Biology and Ecology, Section of Botany, University of Jaén, Campus Universitario

Las Lagunillas s/n. 23071, Jaén, Spain 2. Dpt. of AGRARIA, “Mediterranea” University of Reggio Calabria,

Localita Feo di Vito, 89122 Reggio Calabria, Italy 3 Dpt. of Mathematics, Applied Mathematics area, Univer-

sity of Jaén, Campus Universitario Las Lagunillas s/n. 23071, Jaén, Spain 4 Dpt. of Landscape, Environment
and Planning/Institute of Mediterranean Agricultural and Environmental Sciences (ICAAM), University of
Evora, Rua Roméo Ramatho, Portugal 5 Faculty of Sciences and Technology, University of Algarve, Campus de
Gambelas, 8005-139 Faro, Portugal 6 Centre of Marine Sciences (CCMAR), University of Algarve, Campus
de Gambelas, 8005-139 Faro, Portugal

Corresponding author: Carmelo Maria Musarella (carmelo.musarella@unirc.it)

Academic editor: P de Lange | Received 4 October 2018 | Accepted 6 November 2018 | Published 11 December 2018

Citation: Musarella CM, Cano-Ortiz A, Pinar Fuentes JC, Navas-Urena J, Pinto Gomes CJ, Quinto-Canas R, Cano E,
Spampinato G (2018) Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on
the fractal dimension. PhytoKeys 113: 79-95. https://doi.org/10.3897/phytokeys. 113.30330

Abstract

The fractal dimension (FD) is calculated for seven species of the genus Quercus L. in Calabria region
(southern Italy), five of which have a marcescent-deciduous and two a sclerophyllous character. The fractal
analysis applied to the leaves reveals different FD values for the two groups. The difference between the
means and medians is very small in the case of the marcescent-deciduous group and very large when these
differences are established between both groups: all this highlights the distance between the two groups
in terms of similarity. Specifically, Q. crenata, which is hybridogenic in origin and whose parental species
are Q. cerris and Q. suber, is more closely related to Q. cerris than to Q. suber, as also expressed in the
molecular analysis. We consider that, in combination with other morphological, physiological and genetic

parameters, the fractal dimension is a useful tool for studying similarities amongst species.

Keywords

deciduous, dimension, fractal analysis, phenotype, sclerophyllous, species, Calabria

Copyright Carmelo Maria Musarella et al. This is an open access article distributed under the terms of the Creative Commons Attribution License
(CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

80 Carmelo Maria Musarella et al. / PhytoKeys 113: 79-95 (2018)

Introduction

Quercus L. is an important genus containing several species of trees dominating dif-
ferent forest communities. The ecological and economic role of Quercus spp. is well
known (Quinto-Canas et al. 2010, 2018, Vila-Vicosa et al. 2015, Pifiar Fuentes et al.
2017, Spampinato et al. 2016, 2017, Vessella et al. 2017). Some species (such as cork
oak) are specifically very useful for carbon sequestration and as raw materials for a post
carbon city (Del Giudice et al. 2019, De Paola et al. 2019, Malerba et al. 2019, Mas-
simo et al. 2019, Spampinato et al. 2019).

In the genus Quercus have been counted between 300 (Lawrence 1951, Elias 1971)
and 600 species (Soepadmo 1972). However, several inventories (Schwarz 1964, Nixon
1993, Valencia 2004, Menitsky 2005) amount between 396 and 430 species for this
critical genus. According to Musarella and Spampinato (2012a,b) in Calabria region
(Southern Italy), there are 11 taxa: Quercus ilex L. subsp. ilex, Q. suber L., Q. congesta
C.Presl., Q. cerris L., Q. frainetto Ten., Q. robur L. subsp. brutia (Ten.) O.Schwarz., Q.
virgiliana (Ten.) Ten., Q. amplifolia Guss., Q. dalechampii'Ten., Q. crenata Lam. and Q.
petraea (Matt.) Liebl. subsp. austrotyrrhenica Brullo, Guarino & Siracusa. Bartolucci et
al. (2018) record 17 taxa for Italy (9 of these sure for Calabria). Unfortunately, these au-
thors do not consider in their checklist some species, such as Q. virgiliana and Q. crenata.
However, we consider that Q. virgiliana is present in Calabria and it is clearly distinct
from Q. pubescens Willd. subsp. pubescens according to Brullo et al. (1999), Viscosi et al.
(2011) and Brullo and Guarino (2017). This species plays a very important role in the
forest vegetation of the region (Brullo et al. 2001) and characterises the habitat 91AA*:
Eastern white oak woods (AA.VV 2013, Biondi et al. 2009) distributed in Italy and in
the Balkan Peninsula. Moreover, we consider Q. crenata as a species of hybrid origin from
Q. cerris and Q. suber, according to Conte et al. (2007) and Brullo and Guarino (2017).

Leaf morphology has been studied throughout the history of botany, using leaf
shape, edge, vein arrangement, hairiness and other features as important characters
in systematics (Coutinho 1939, Amaral Franco 1990). Species have been described
by means of the analysis of the size and shape of several leaf characters and using bio-
metric studies. Morphometry and the leaf vascular system have traditionally been key
aspects for establishing the description and biometrics of the species; in morphometry,
the leaf shape and edge and the arrangement of the veins are all common systematic
characters used to characterise different species. For a correct determination of each
species and their hybrids, their taxonomic characters must be observed with specific
instruments, e.g. powerful microscopes capable of highlighting micromorphometric
characters (Vila-Vicosa et al. 2014).

Numerous authors have noted the comparative inaccuracy of early descriptive and
biometric studies (Mouton 1970, 1976, Hickey and Wolfe 1975, Hickey 1979). Clas-
sic descriptive methods do not establish clear differences between pure individuals and
their hybrids, so molecular studies are proposed for pure and hybrid strains (Conte
et al. 2007, Curtu et al. 2007, Coutinho et al. 2014, 2015). More precise biometric
studies subsequently emerged that allowed a more meticulous representation of the leaf

Similarity analysis between species of the genus Quercus L. (Fagaceae) in... 81

detail or the other parts of the plants (e.g. Cano et al. 2017). Biometrics thus came into
its own for pinpointing the differences between species and taxonomic groups.

In their study of several Quercus species, Camarero et al. (2003) and Fortini et al.
(2015) analysed the leaf morphology for pure and hybridogenic populations and ob-
served the variability of their morphological characters. These phenotypical characters
must be precisely quantified to establish the differences between pure species and their
hybrids, which can be recognised through fractal analysis.

We calculated the fractal dimension by the box-counting method integrated in the
Image] software (Abramoff et al. 2004), as it allows the possibility of assessing the frac-
tal dimension of structures that are not totally self-similar. To resolve the controversy
regarding certain species/subspecies in the genus Quercus, a discriminant analysis is
required that can clearly differentiate the species/subspecies and the degree of relation-
ship between them. The fractal dimension, which has not so far been widely applied in
botany, although somewhat more so in medicine, was used for this purpose (Esteban
et al. 2007, 2009, Lopes and Beltrouni 2009).

The main aim of this work is to establish an analysis of similarity of leaf shape
amongst seven species in the genus Quercus from Italy and corroborate our previous
studies (Musarella et al. 2013), in which we proposed a FD < 1.6 for sclerophyllous
Quercus and FD > 1.6 for deciduous and marcescent Quercus.

Methods

Data collection

In this work, we analysed 7 species living in Calabria using 275 tree samples belonging to
Quercus robur subsp. brutia, Q. cerris, Q. congesta, Q. crenata, Q. ilex subsp. ilex, Q. suber
and Q. virgiliana. Orientation largely determines the amount of light the leaves receive for
photosynthesis and their size can thus be affected by this greater or lesser exposure to light.
For this reason, samples were taken from the four cardinal points on each tree to examine
the possible influence of orientation on leaf development. A total of 1,099 leaves were
analysed from 120 samples of Q. robur subsp. brutia, 120 from Q. cerris, 154 from Q. con-
gesta, 147 from Q. crenata, 240 from Q. ilex subsp. ilex, 139 from Q. suber and 179 from
Q. virgiliana. All the leaves were colour-scanned in a scanner with a resolution of 1200
dpi and 24-bit colour. After scanning, the leaf was transformed to image 8-bit greyscales
and the image was segmented by selecting the greyscale between 111 and 126. We opened
this image with the Image] programme in order to determine its fractal dimension (FD).

The fractal dimension (FD)

Fractal geometry is the most suitable method for characterising the complexity of the
vascular system or other mathematically similar structures such as stream drainage net-

82 Carmelo Maria Musarella et al. / PhytoKeys 113: 79-95 (2018)

works in chicken embryos or the distribution of the vascular system of a leaf (Horton
1945, Vigo et al. 1998). De Araujo Mariath et al. (2010) developed a method using
digital images of leaves to determine the fractal dimensions of the leaf vascular system
in three species of Relbunium (Endl.) Hook. E (Rubiaceae), with the aim of quanti-
fying and determining its complexity so it could be used as a taxonomic character.
Recently, Cuzzocrea et al. (2017) described an algorithm to estimate the parameters of
Iterated Function System (IFS) fractal models, using IFS to model speech and electro-
encephalographic signals and to compare the results.

All man-made objects can be described in simple shapes using Euclidean geometry.
However, natural objects have irregular forms that cannot always be represented using
this method (Glenny et al. 1985).

Due to the recentness of the discovery and its wide range of applications, there
is still no universal definition of what actually constitutes a fractal. They are thus de-
scribed according to their common properties: specifically, they must have the same ap-
pearance at any scale of observation, meaning that a fractal object can be broken down
into parts, each of which is identical to the whole object (self-affinity or self-similarity);
they must have a fractional and not a whole dimension (fractal dimension); and fi-
nally the relationship between two of their variables must be a power law (where the
exponent is its fractal dimension, Mandelbrot 1983). Topological and Euclidean di-
mensions cannot be applied to highly irregular objects such as coastlines. Mandelbrot
(1967) published a widely-referenced work where he proved that it was impossible to
give an exact value of the length of the coast, as this measurement depended on the unit
of scale used. Thus in the case of irregular curves, a small FD of close to 1 signifies a low
level of complexity, whereas values close to 2 indicate a very high level of irregularity.

When an object is totally self-similar, such as the mathematical fractal known by
the name of the Koch curve (Figure 1), the dimension used is known as the self-
similarity dimension.

A unit segment can be divided — for example — into three pieces similar to the
original, each with a length of 1/3. In general, where N(h) is the number of pieces
with a length /, it follows that N(h) - 4' = 1. If we now look at a square with a unit
side, we can break it down into 9 = 3* smaller squares with a side of 4; that is to say
N(h) : /° = 1. Finally, in the case of a cube, it is easy to see that the following is true:
N(h) - b° = 1. That is, the exponent of / coincides with the topological and Euclidean
dimension of the straight line (1), the square (2) and the cube (3) (Martinez Bruno
and de Oliveira Plotze 2008).

Figure |. The Koch curve.

Similarity analysis between species of the genus Quercus L. (Fagaceae) in... 83

By extrapolation from this concept, if the object is completely self-similar, there is
a relationship between the scale factor / and the number of pieces V(/) into which the
object can be divided, which is given by N(h) = (1//)”; that is to say

i logiN(h))
log(=)
Thus the fractal dimension of the Koch curve is:

—__ logi4)
Te)

= 1.2619,

a number that is very similar to the FD of the English coastline.

However, natural objects like leaves are not perfect fractals, as they are not totally
self-similar but are said to be statistically similar. In this case, the value of their fractal
dimension is known by the name of Hausdorff-Besicovitch and is:

: logiN(h))
D= lim, 5 Togs) :

The calculation of this limit is somewhat complicated and requires the use of dif-
ferent algorithms such as dilation methods, the perimeter method, Grassberger and
Procaccia’s correlation dimension and box-counting method. This last is the most
widely used as it is very simple to implement with computer technology and highly
accurate (Glenny et al. 1985, Jian Li et al. 2009).

To find the fractal dimension of a digital image using the box-counting method
(Mandelbrot 1983), the image must be transformed into black (the leaf) and white
(the background). A grid is then superimposed on the image and the number of times
the leaf intersects a grid square is counted. ‘The image is covered with a grid of squares
initially with side 2 and subsequently with squares with side 3, 4, 6, 8, 12, 16 and 32
(in Table 1; C2, C3, C4, C6, C8, C12, C16 and C32). The side of square / is then
reduced and the logarithm of the number of intersections N(h) is represented based on
the logarithm of the inverse function of the side. The dimension of the object coincides
with the slope of the regression line defined by the point cluster (log(I/h), log(N(h))
produced when the value of the side of the grid square is changed.

The graphic representation of the regression line and the point cluster shows two
very clearly differentiated parts. The minimum and maximum box size is therefore
very important when applying this method. In fact, the approximation error must be
reduced by selecting points with a “more linear” form as a box size.

Calculating the fractal dimension (FD)

The FD was calculated by the box-counting method (Esteban et al. 2007) using the free
software Image] version 1.47 (http://imagej.com). The digital image of the leaf in RGB col-

84 Carmelo Maria Musarella et al. / PhytoKeys 113: 79-95 (2018)

Table I. Number of boxes occupied for each box size.

Label C2 C3 C4 C6 C8 C12 C16 C32 D
QCONGESTAI_E_01 358874 ~—- 166858 97125 44308 25268 11452 6553 1727 1.93

Figure 2.a RGB colour image b 8-bit greyscale image and € binary selection of an image of a Quercus
crenata leaf.

our (Figure 2a) was first converted into an 8-bit image (Figure 2b) where each pixel was rep-
resented with a greyscale from 1 to 256. In order to select the most important information,
the image was subsequently segmented to produce a greyscale between 111 and 126 and
then converted into binary so the leaf takes the value 1 and the rest the value 0 (Figure 2c).

The box-counting algorithm was then applied to this black-and-white image of the ve-
nation network of the leaf to calculate the FD with box sizes (4) ranging from 2 to 32. Spe-
cifically, the image is covered with a grid of squares initially with side 2 and subsequently
with squares with sides 3, 4, 6, 8, 12, 16 and 32 (in the image C2, C3, C4, C6, C8, C12,
C16 and C32). Table 1 shows the number of boxes occupied (V(h)) for each box size.

Once the points were represented (/log(I/h), log(N(h)), we calculated the regression
line (Figure 3) whose slope corresponds to the value of the fractal dimension; in our
case, the FD=1.9298, Standard Error= 0.0044, p-Value=1.01384*104(-14). As can
be seen in the graph, the fit is fairly good as the points are very close to the resulting
regression line.

For the statistical treatment, the mean FDs were obtained for each species and
an analysis of variance was undertaken to test for significant differences amongst the
means. First, the Shapiro-Wilk normality test and the difference between the mean,
median and kurtosis indicate that our data do not follow a normal distribution (Ta-
ble 2), meaning non-parametric methods must be used. To determine whether orien-
tation affects the leaf morphological character, we applied a non-parametric Kruskal-
Wallis test which, based on the medians, compares the leaves from the same population

Similarity analysis between species of the genus Quercus L. (Fagaceae) in... 85
Table 2. Descriptive statistics of FD values for each species and orientation.

Taxa Kurtosis St. root of the St. root

(Pearson) variance [kurtosis

(Fisher) ]

North | Q. robur subsp. brutia 0.8327
Q. cerris 0.8327

Q. congesta 0.7587

Q. crenata 0.7497

Q. ilex subsp. ilex 0.6133

07879
0.6876

Sou 08327
08597
07587
07497
0.6133
Q. suber 0.7879

Q. virgiliana 0.6876

East | Q. robur subsp. brutia 0.8327
Q. cerris 0.8327

Q. congesta 0.7587

Q. crenata 0.7497
Q. ilex subsp. ilex 0.6133
Q. suber 0.7879
0.6876
Wes 08327
058397
07587
07497
0.6133
07879
Ova 0.6876

Mean | Q. robur subsp. brutia 138.47.00
Q. cerris 0.8327
Q. congesta 0.7587
Q. crenata 0.7497
Q. ilex subsp. ilex 0.6133
07879
0.6876

log (count)

1.0

a

1.5

2.0
log (box size)

Figure 3. Regression line for the points (log(1/h), log(N(h)).

2.0

3.0

86 Carmelo Maria Musarella et al. / PhytoKeys 113: 79-95 (2018)

and from the four orientations. We also applied the standardised kurtosis coefficient to
determine whether there is significant normality in the data. In the case of significant
differences in the analysis of variance, we applied the LSD (Least Significant Differ-
ence) multiple comparison test.

In the hypothetical case that the difference between the fractal values (means and
medians) for two species is zero or has a quotient of one, the degree of relationship
between the two species is 100%; DfA — DfB = 0; DfA / DfB = 1, species A and B are
equal; thus the lower the fractal difference or the nearer the fractal quotient is to 1, the
greater the similarity between the species.

Results

The analysis of the FD values for each orientation and for each species shows that for
Q. robur subsp. brutia, Q. cerris, Q. congesta and Q. virgiliana, the orientation influ-
ences the values of FD, as there are significant differences for these species (Table 3).

These species correspond to deciduous or marcescent species, whereas the peren-
nial species Q. ilex subsp. ilex, Q. suber and Q. crenata do not show significant differ-
ences in the values of FD for the different levels of orientation.

Table 3. Kruskal-Wallis analysis for the values of FD in each orientation for each of the species. In bold:

the significant values for which orientation influences the FD at 95% confidence.

Kruskal-Wallis: echt coe Q. cerris Q. congesta Q. crenata Q ae *“— Qsuber — Q. virgiliana
Mean North 1.5290 1.6676 1.8310 1.8669 1.3804 0.9001 1.9192
Mean South 1.6220 1.6190 1.8749 1.8803 1.3442 0.9487 1.8780
Mean East 1.7336 1.8110 1.9215 1.8476 1.3276 0.9059 1.9287
Mean West 1.5676 1.6116 1.8985 1.8754 1.3895 0.9746 1.9317
St. Deviation North 0.2702 0.1936 0.1174 0.1313 0.1723 0.2651 0.0406
St. Deviation South 0.2992 0.1836 0.0763 0.1030 0.1220 0.2020 0.0777
St. Deviation East 0.2069 0.1194 0.0288 0.1602 0.1074 0.2180 0.0563
St. Deviation West 0.2829 0.2535 0.0546 0.0921 0.1564 0.2479 0.0392
K (Observed value) 9.9875 20.5115 23.0332 1.6844 8.0795 3.0683 38.4400
K (Critical value) 9.4877 7.8147 7.8147 7.8147 9.4877 7.8147 7.8147
p-value 0.0406 0.0001 < 0.0001 0.6404 0.0887 0.3812 < 0.0001
Table 4. Kruskal-Wallis test.

K (Observed value) 220.2702

K (Critical value) 12.5916

GDL 6

p-value (bilateral) < 0.0001

alpha 0.05

Similarity analysis between species of the genus Quercus L. (Fagaceae) in...

87

Table 5. Differences in FD by pairs between each species (in parentheses, p-value). In bold: significant
differences at 95% confidence.

Q. robur subsp. Q. cerris Q. congesta Q. crenata Q. ilex subsp. Q. suber Q. virgiliana
brutia ilex
Q. robur -
subsp. brutia
Q. cerris 4.26 (0.6392)
Q. congesta 71.21 66.95
(<0.0001) (<0.0001)
Q. crenata 68.55 64.29 -2.65 (0.7439)
(<0.0001) (<0.0001)
Q. ilex subsp. -58.63 -62.9 (<0.0001) -129.85 -127.19
ilex (<0.0001) (<0.0001) (<0.0001)
Q. suber -109.43 -113.7 -180.65 -177.99 -50.8 (<0.0001) -
(<0.0001) (<0.0001) (<0.0001) (<0.0001)
Q. virgiliana 96.87 92.61 25.66 (0.001) | 28.32 (0.0002) 155.51 206.31 =
(<0.0001) (<0.0001) (<0.0001) (<0.0001)
Box plots
Fractal
dimension
1,9 | aa 1,8814 ma 1,8675 114 SS
17 4 —( 1,6773
1,6130 | + fey
aan
1,3604
143 --
1,1 4
0,9 + 0,9328
0,7 !
05 |
Q.robur subsp. brutia Q. cerris Q. congesta Q.crenata Q. ilex subsp. ilex Q. suber Q. virgiliana
+ Mean

Figure 4. Value of the medians for each homogeneous group. Fractal dimensions (mean values) of the
studied species where Quercus ilex subsp. ilex and Quercus suber have an FD < 1.6 and the marcescent

Quercus has a FD > 1.6.

An analysis of the average FD values for each species indicates that there are sig-
nificant differences between the different levels of species under study (Table 4). Sub-
sequently, the Conover-Iman test of multiple comparisons between all pairs shows the
pairs of species between which there are significant differences (Table 5).

As can be seen in Table 5, there are pairs of species for which there are significant
differences in the values of FD. These differences are not only significant between the
species Q. robur subsp. brutia - Q. cerris and between Q. crenata - Q. congesta. The frac-
tal dimension is therefore sufficient alone to characterise and separate the species Q.

88 Carmelo Maria Musarella et al. / PhytoKeys 113: 79-95 (2018)

ilex subsp. ilex, Q. suber and Q. virgiliana, while the fractal dimension of the vascular
network of the leaves calculated by the methodology described does not distinguish Q.
robur subsp. brutia from Q. cerris and Q. congesta from Q. crenata on its own.

The analysis of the medians of the seven groups (Figure 4) shows that the lowest
values of FD correspond to the sclerophyllous Quercus species Q. ilex subsp. ilex and
Q. suber, whose values are below 1.6, as occurs in the case of the medians. However the
marcescent Quercus have a median FD of > 1.6; the mean FD values of Q. suber and Q.
ilex subsp. ilex are 0.932 and 1.363, respectively, whereas it is 1.613 for the marcescent
Q. robur subsp. brutia; 1.677 for Q. cerris; 1.881 for Q. congesta; 1.868 for Q. crenata;
and 1.914 for Q. virgiliana.

In the multiple comparison analysis (Figure 5) of means and medians, the most
significant differences in the two cases are between the sclerophyllous and marces-
cent Quercus, where these differences (means) are 0.982 for Q. virgiliana-Q. suber and
*0.984 in the case of the medians; however the differences between the marcescent
Quercus are minimal with *0.015 for Q. congesta-Q. crenata and *0.188 between Q.
cerris-Q. crenata. As the value for Q. crenata-Q. suber is *0.939, it is evident that Q.
crenata is more closely related to Q. cerris than to Q. suber (Figure 5).

In the case of both mean and median values, it is confirmed that the value of the
fractal dimension (FD) is less than 1.6 in the case of sclerophyllous Quercus and greater
for marcescent and deciduous Quercus (Figure 4).

The differences between average FD values for marcescent and deciduous Quercus
species are very low (Table 6). These low differences between average FD values are due
to the close similarity between these species. However, there are significant differences
in the FD between marcescent and sclerophyllous Quercus as they are very distant from
each other in evolutionary terms: Q. virgiliana-Q. ilex subsp. ilex 0.551; Q. virgiliana-

Ww
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Figure 5. Multiple comparison analysis.

Similarity analysis between species of the genus Quercus L. (Fagaceae) in...

Table 6. Homogeneous character of the groups.

Species

Q. suber
Q. ilex subsp. ilex
Q. robur subsp. brutia

Count | Sum of the ranges

Mean of the ranges

ee al groups

£26,0000
4083.5000 69.2119 B ia

3835.5000

127.8500

Q. cerris 3963.5000 132.1167
Q. crenata 7463.5000 196.4079

. congesta 7365.5000 199.0676
Q cong

89

10337.5000 224.7283

Q. virgiliana

Q. suber 0.982; Q. congesta-Q. ilex subsp. ilex 0.518; Q. congesta-Q. suber 0.949; Q.
crenata-Q. ilex subsp. ilex; 0.505; Q. crenata-Q. suber 0.936; Q. cerris-Q. ilex subsp. ilex
0.314; Q. cerris-Q. suber 0.745; and Q. ilex subsp. ilex-Q. suber 0.431.

Based on the differences obtained from FDA—FDB = 0, the most closely related
species are: Q. congesta-Q. crenata 0.023; Q. cerris-Q. robur subsp. brutia 0.064; Q.
virgiliana-Q. congesta 0.033; Q. virgiliana-Q. crenata 0.046; and Q. crenata-Q. cerris
0.191. The most distant relationship is between Q. virgiliana-Q. suber 0.982 and Q.
congesta-Q. suber 0.949 (Figure 5).

Discussion

There is a widespread consensus that complex objects with the same features can be
included in the category of fractals. Self-similarity is one of the characteristics of fractal
objects, meaning that when these images are broken down into smaller pieces, each
one is identical to the whole. The fractional dimension is another of its features.

In the hypothetical case that the difference between the fractal values of two species is
zero, or their quotient is one, the degree of relationship between the two species is 100%:
Df, = Df, = 0; Df, / Df, = 1, species A and B are equal. Thus the smaller the fractal dif-
ference or the closer the fractal quotient is to 1, the greater the similarity between the spe-
cies; if the value of this quotient is far from 1, as occurs between Df, il Df. ees the species
Q. virgiliana and Q. suber are very distant from each other. This occurs when the fractal
values are the same and means that the same or similar characters have been measured

Conte et al. (2007) point out the hybridogenic origin of Q. crenata and the mo-
lecular analysis reveals a closer genetic similarity between Q. crenata and Q. cerris
than between Q. crenata and Q. suber. The FD of Q. crenata is 1.868; for Q. cerris it
is 1.677; and for Q. suber it is 0.932; where Diss = Dis. = 0.745 and Dia. / Diss
= 1.8, pointing to a large phenotypical (genetic) difference between the parental spe-
cies. More similarity can be seen between Q. crenata and Q. cerris than between Q.
crenata and Q. suber, as the difference Dee = Diy. = 0.191 and Dios / Dik = 1.1;
they therefore have a high degree of similarity; whereas Die. a Dis. = 0.936 and
Df, / Df,,, > 2, indicating substantial phenotypical differences between the hybrid

and iparehtal species.

90 Carmelo Maria Musarella et al. / PhytoKeys 113: 79-95 (2018)

Coutinho et al. (2014, 2015) report a high degree of polymorphism in the genus
Quercus and establish the molecular analysis of ribosomal DNA through the restriction
enzymes to confirm the taxonomic classifications and establish the phylogeny between
Quercus species. Their results show that the group known as cerris contains Q. crenata
and its parental species Q. cerris, whereas it excludes the parental species Q. suber; Q.
crenata is closer to Q. cerris with a similarity of 96% compared to a 66% similarity
between Q. suber and the previous species. Our fractal analysis corroborates the results
of Conte et al. (2007) and Coutinho et al. (2015). Curtu et al. (2007) studied four oak
species, including Q. robur and Q. cerris and the intermediate or hybridogenic forms
using morphological leaf and genetic markers to classify the hybridisation. In our case,
the intermediate or hybrid form corresponds to Q. crenata which has its origins in the
parental species Q.cerris and Q. suber. Here the intermediate form Q. crenata has a
fractal value close to Q. cerris and very far from Q. suber.

Finally, the orientation has no influence on the fractal dimension between either the
same species or between the different species. This means that the shape of the distribu-
tion of the leaf vascular network is not affected by possible changes in orientation, thus
discounting the effects of environmental variables such as amount of light, temperature,
humidity etc., associated with orientation. This evidence is important in Quercus spe-
cies, as in other cases, these environmental variables can influence seed germination and
the capacity of some plant species to adapt to extreme environments (Signorino et al.
2011, Musarella et al. 2018, Panuccio et al. 2018, Spampinato et al. 2018): in some
cases, the survival or disappearance of a species in an environment may depend on it.

Conclusions

We confirm that the application of fractal analysis identifies the phenotypical differ-
ences between species and can be used as a method to establish their degree of rela-
tionship; this is supported by molecular analysis by various authors. In this work we
can affirm that sclerophyllous Quercus species have a fractal dimension of < 1.6 and
marcescent and deciduous Quercus species have FD > 1.6; and that Q. crenata, a hy-
brid of Q. suber and Q. cerris, has a greater similarity to Q. cerris than to Q. suber. The
low values of the mean and median FD revealed by the differences between the FD
for marcescent-deciduous Quercus species suggest a high degree of similarity amongst
the five marcescent-deciduous species. Based on their FD, marcescent Quercus species
(semideciduous) are more closely related to deciduous than to sclerophyllous Quercus
species, whereas the sclerophyllous Q. ilex subsp. ilex and Q. suber show substantial
morphological differences with the marcescent and deciduous Quercus species, as evi-
denced by fractal analysis. These two species have followed different evolutionary paths
from the others, as is to be expected, as the centre of origin of sclerophyllous Quercus
species is Mediterranean, whereas deciduous Quercus species have a temperate origin
and marcescent Quercus species come from the boundary between the Temperate and
Mediterranean bioclimates (Amaral Franco 1990, Sanchez de Dios et al. 2009).

Similarity analysis between species of the genus Quercus L. (Fagaceae) in... 91

Acknowledgements

We are very grateful to the anonymous referees and to Subject Editor Peter de Lange
for their suggestions for improving the original article. This article has been translated
by Ms Pru Brooke-Turner (M.A. Cantab.), a native English speaker specialising in

scientific texts.

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